BBC political correspondent Jonathan Blake said the prime minister spent Sunday meeting his closest advisers at the government's countryside residence Chevening House, in Kent, "perhaps planning the next move".

Ms Rudd told the Sunday Times she would be considering whether to stand as an independent Conservative should there be an general election.

In her resignation letter to the prime minister, Ms Rudd said: "I joined your cabinet in good faith: accepting that no-deal had to be on the table, because it was the means by which we would have the best chance of achieving a new deal to leave on 31 October.

"However, I no longer believe leaving with a deal is the government's main objective."

She called the PM's decision to expel 21 MPs from the parliamentary Conservative party an "act of political vandalism", after her former colleagues rebelled last week over a bill designed to avoid a no-deal Brexit.

"If we become a party which has no place for the type of moderates that I am, the centre-right Conservatives, then we will not win [a general election]," she said.

Analysis: 'More ministers contemplating resigning'

by John Pienaar, BBC deputy political editor

Amber Rudd's resignation was symptomatic of a deeper struggle going on inside the government and inside the Conservative Party.

Whatever anyone says, a number of ministers are considered to be privately unhappy with the government's strategy and contemplating the possibility of resigning in the wake of Amber Rudd's resignation.

The former chancellor, Philip Hammond, was saying this weekend that usurpers were turning the Tory party into an extreme right-wing sect.

He was clearly referring to people like the prime minister's famously abrasive, divisive adviser, Dominic Cummings.

But there's no sign of the inner circle in No 10 relenting or repenting - just the opposite.

One minister said to me today: "Look at the opinion polls. Tories well ahead - it's working." Losing colleagues, to him, was collateral damage.

Ms Rudd, the MP for Hastings and Rye, who supported Remain in the 2016 referendum, has resigned the Tory whip - meaning she will remain an MP but no longer sit as part of the Conservative party in Parliament.

She told the BBC there was "very little evidence" the government would get a new Brexit deal, and she had only received a "one-page summary" of efforts to get an agreement when she asked for details earlier this week.

She said "proper discussions about policy" had not been taking place, suggesting senior ministers had limited involvement in the PM's decisions.

Cabinet ministers had also not been shown legal advice to the prime minister about his decision to prorogue - or suspend - Parliament from next week until 14 October, Ms Rudd said.

Asked who was running the country, if not the cabinet, she replied: "If I knew that, I would perhaps have had further conversations with the prime minister, or them."

Labour Party chair Ian Lavery said the resignation was a sign that "no one trusts" Mr Johnson. "The prime minister has run out of authority in record time and his Brexit plan has been exposed as a sham," he said.

SNP Westminster leader Ian Blackford called on the prime minister to resign, arguing he had "no support or credibility left".

But Foreign Secretary Dominic Raab said Mr Johnson had made clear to all his cabinet ministers they needed to support his policy of leaving the EU by 31 October, in all circumstances.

"We all accepted that, and I think the prime minister was right to restore some discipline - and I think he's right to expect it from his top team," he told Sky News.

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Media captionSajid Javid: "We are working wholeheartedly, straining every sinew, to get a deal"

In other developments:

Senior ministers insist Mr Johnson won't break the new law which says he must seek a Brexit extension from the EU if no new deal has been agreed by 14 October - but the UK will still leave with or without a deal on 31 October